What effect did Samurott have on the metagame?
Ever since being really "discovered" a couple of months into NU's existence, Samurott has been a consistently dangerous threat that every team in every NU metagame
needs to be prepared for. No matter which point of NU's history you pick out, Samurott has always been one of the most threatening and versatile weapons to have on your side (and one of the most important Pokemon to keep in mind when you're teambuilding). Though the usage stats don't necessarily show complete dominance over the metagame, there's no doubt that Samurott is far and away among the scariest threats in NU.
In what main roles was Samurott used?
Samurott was initially used as the tier's premier physical Water-type. Swords Dance primed Samurott for a quick sweep after you weakened its few checks, and Megahorn gave it a superb coverage move. Not many other Pokemon can offer a base 120 attack with near-flawless neutral coverage with their STAB attack. Additionally, Samurott packed Aqua Jet to alleviate its somewhat mediocre Speed and to make sweeps possible.
After a bit of experimentation and noticing that Samurott's highest stat was in fact its Special Attack, various people popularized specially offensive Samurott, which is just as dangerous as the physical variant, if not moreso. Special Samurott annihilated all of the physical set's counters, allowing it to act as a lure for other Pokemon and also serve as a phenomenal attacker on its own.
What caused Samurott to have a significant impact?
Samurott's dominant sets have been very flexible and reacted strongly to how the metagame has developed, meaning that no matter how the metagame played, Samurott was able to hold its own. For example, early on in NU, Samurott's SD set was easily the most dominant (and for good reason!). As the metagame played out, people started preparing heavily for it, which would make any normal Pokemon much less effective... but Samurott's sets adapted to this and suddenly the more popular set was the special one, because just about everyone had Quagsire / Alomomola / Altaria etc on their team to beat out the physical variant. The metagame had also slowed down significantly after Jynx had left, leaving SD Samurott out to dry a little bit because the priority of Aqua Jet was less of an advantage over the raw power of special Samurott.
Its favored spread and item have also been very adaptive over time to show that literally nothing could slow it down. Lum Berry became popular on SD sets as Alomomola gained popularity, and Megahorn found its way into special sets when suddenly Ludicolo became the one true plausible stop to special Samurott. Samurott has also jumped around between Life Orb and Mystic Water, as well as between bulkier Adamant / Modest spreads and Jolly / Timid spreads as each metagame developed. Samurott's stat build and movepool has allowed it to be diverse and adaptive to every single metagame that has existed, being a significant threat in every single one.
Samurott has always been a very consistent, very dangerous Pokemon to have on your team. Its versatility and power is unmatched in NU and it has excelled since the dark ages of Klinklang and Magmortar.
How do/did you deal with Samurott in NU?
Samurott is easily one of the most challenging Pokemon to deal with in NU. Identifying the set is by far the most important step; both the special set and physical set have completely different counters. For the physical set, Alomomola, Quagsire, physically defensive Amoonguss and fast Pokemon that resist Aqua Jet have probably been the most ideal responses through time. Samurott can also be revenged by a number of faster Pokemon that can live a +2 Aqua Jet, such as Eviolite Electabuzz, Simipour, Simisage, and Rotom-A (it's OHKOed after two SR switch-ins though!). However... nearly all of these counters are demolished by special Samurott, which is really only stuffed by a handful of specially defensive Pokemon, such as Regice, Ludicolo, and Articuno. The real trick has always been figuring out what kind of Samurott your opponent has, and hoping that they don't carry a trick move to beat your only counter for that variant of Samurott. Taunt / Substitute SD Samurott has been used to set up all over Alomomola, Megahorn and Superpower have been carried on special sets for Ludicolo and Regice / Lickilicky...